Introduction

Question

How to select superior soybean genotypes across locations and years (GxE interaction) according to Multitrait ideotype? (Simultaneous selection)

Hypothesis

Estimate probability of superior performance (Dias et al. 2022) across locations and years and classify genotypes using Bayesian Probabilistic Selection Index (Chagas et al. 2025)

Goal

Important

Select superior soybean genotypes to grain yield, plant height and plant lodging using Bayesian probabilistic selection index (BPSI) (Chagas et al. 2025)

Material and Methods

Ensaios experimentais
  • 14 locations
  • 6 years
  • 41 trials
  • 98 genotypes
  • 3 traits (Grain Yield, Plant Height, Plant Lodging)
  • Randomized complete block design (RCB)
  • Using package ProbBreed (Chaves et al. 2024)

Material and Methods

Individual analyses

\[ \mathbf{y} = \mathbf{X_1b} + \mathbf{Z_1g} + \mathbf{\epsilon} \]

where \(\mathbf{y}\) is the vector of phenotypic observations, \(\mathbf{b}\) is the vector of fixed effects of replication, \(\mathbf{g}\) is the vector of random effects of genotypes and \(\mathbf{\epsilon}\) is the vector of random errors. \(\mathbf{X_1}\), \(\mathbf{X_2}\) e \(\mathbf{Z_1}\) are incidence matrix of \(\mathbf{b}\) and \(\mathbf{g}\) effects respectively..

Material and Methods

Heritability

\[ h^2 = \sigma^2g / \sigma^2g + \sigma^2e \]

where \(\sigma^2g\) is the genetic variance and \(\sigma_e^2\) is the residual variance.

Experimental Coeficient of Variation

\[ CV = \frac{\sigma_e}{\mu} \times 100 \]

where \(\mu\) is the trait mean.

Material e Métodos

Likelihood ratio test

\[LRT= −2 \times (Log𝐿 - Log L_𝑅)\]

where \(L\) is the maximum point of residual likelihood function of the complete model and \(L_R\) is the same for the reduced model, that is, without the effect to be tested. The LRT value was compared with a tabulated value based on the chi-square table, with one degree of freedom and 0.95 probability.

Material and Methods

Bayesian model

\[ y_{jkhp} = \mu + t_h + l_k + b_{p(k)} + g_j + gl_{jk} + gt_{jh} + \varepsilon_{jkhp} \] where the \(y_{jkhp}\) is the phenotypic record of the \(j^{th}\) genotype, allocated in the \(p^{th}\) block, in the \(k^{th}\) location and in the year \(t_{th}\). All other effects were previously defined but \(b_{p(k)}\), which is the effect of the \(p^{th}\) block in the \(k{th}\) location, and \(gl^{jk}\) , which correspond to the genotype-by-location interaction \(t_h\) and \(t_{jh}\) are the main effect of years and the genotypes-by-years interaction effect, respectively.

Material and Methods

Probability of superior performance

BPSI index uses the probability of superior performance to estimate the chance of a genotype being selected in multienvironmental trials (Dias et al. 2022).

\[ Pr\left({\hat{g}}_i \in \Omega \middle| y\right) = \frac{1}{s}\sum_{s=1}^{s} I \left({\hat{g}}_i^{(s)} \in \Omega \middle| y\right) \]

where \(\hat{g}_i\) is the genotypic value, \(\Omega\) is a subset of genotypes with superior performance and \(s\) represents each sample of posterior distribution.

Material and methods

Bayesian Probabilistic Selection Index

\[ BPSI_i = \sum_{m=1}^{t} \frac{RankProbSup^t}{\omega^t} \]

where \(t\) is the total number of traits evaluated \((m =1, 2,…,t)\) and \(\omega\) is a weight. Traits of greater interest will have larger \(\omega\). We used weight 2 for GY and weight 1 for PH and PL. The 10% best-ranked families were selected according to the BPSI.

Genotype T1(Rank) T2(Rank) T3(Rank) PSI
1 10 5 2 ∑ i.= 17
2 5 3 10 ∑ i.= 18
3 7 3 10 ∑ i.= 19

Results

Results

Results

Results

Results

Results

Results

Variances

Results

Variances

Results

Density

Results

Within

Results

Across

Results

Density

BPSI

load("../Saves/res_PL_year.rda")
load("../Saves/res_PH_year.rda")
load("../Saves/res_GY_year.rda")

source("../data/bpsi_fun.R")

models= vector("list",length(3))


models[[1]] = res_GY;
models[[2]] = res_PH
models[[3]] = res_PL
models[[3]]$across$perfo <- models[[3]]$across$perfo[-which(models[[3]]$across$perfo$ID=="G_55"),]
names(models) <- c("GY","PH","PL")
BPSI_soy=BPSI(modlist = models,increase =c(TRUE,FALSE,FALSE),omega = c(2,1,1),int = 0.1,save.df = T,verbose = T )

df=BPSI_soy$BPSI

gen.sel = df[which(df$sel=="selected"),"gen"]


real.names=distinct(pheno[,c(5,15)])

df <- left_join(df, real.names, by = c("gen" = "geno"))

print(df)
     GY   PH   PL  bpsi      sel  gen   Crop_Variety
1   0.5  4.0  4.0   8.5 selected G_20           Opal
2   8.0  6.0  4.0  18.0 selected  G_3          Bimha
3   3.0  2.0 17.5  22.5 selected G_38       SBV15043
4   7.0  5.0 18.0  30.0 selected G_45      SC SIESTA
5  13.0  3.0 15.0  31.0 selected  G_4    CBI1055/6/6
6   7.0  8.0 24.5  39.5 selected G_13        Mhembwe
7  29.0 12.0  5.0  46.0 selected G_16        Mwenezi
8  19.0 18.0 14.0  51.0 selected  G_1       1075/6/2
9   2.0 49.0  1.5  52.5 selected G_32    S1195/6/105
10 19.0 21.5 12.0  52.5 selected G_33    S1219/6/116
11 27.0  7.0 19.0  53.0  not_sel G_14          Mhofu
12 15.0 38.0  4.5  57.5  not_sel G_21       Pan 1867
13 10.0 17.0 33.0  60.0  not_sel G_31     S1187/5/37
14 57.0  1.0  2.5  60.5  not_sel G_54         SSS500
15  2.0 52.0  7.0  61.0  not_sel G_50        SC SZ01
16 17.0 17.5 28.0  62.5  not_sel G_28     S1150/5/22
17 48.0  3.5 11.0  62.5  not_sel G_64  TGx 2002-14DM
18  5.0 47.0 13.0  65.0  not_sel G_93  TGx 2053-22FZ
19 13.0 42.0 13.5  68.5  not_sel G_40      SC SAFARI
20 34.0 24.0 11.5  69.5  not_sel G_49      SC STATUS
21 23.0 25.0 23.0  71.0  not_sel G_60 TGx 2000-305GZ
22 37.0 18.0 17.0  72.0  not_sel G_39       SBV15062
23 20.5 39.0 13.0  72.5  not_sel G_68   TGx 2002-9FM
24 36.0 29.0  8.0  73.0  not_sel  G_8        Lukanga
25 24.0 34.0 18.5  76.5  not_sel G_77 TGx 2023-301GZ
26  3.0 61.0 20.0  84.0  not_sel G_53     SI273/6/65
27 18.0 24.0 47.0  89.0  not_sel G_36     S1275/6/59
28 21.0 38.0 30.0  89.0  not_sel G_47       SC SPIKE
29 33.0 20.5 38.0  91.5  not_sel G_52          SCS-1
30 23.0 30.0 39.0  92.0  not_sel G_29     S1180/5/54
31  9.0 28.0 55.0  92.0  not_sel G_44    SC SERENADE
32 14.0 76.0  2.0  92.0  not_sel  G_9          Lundi
33 32.0  9.5 51.0  92.5  not_sel G_11      MAKSOY 5N
34 43.0 28.0 21.5  92.5  not_sel G_74  TGx 2014-52GZ
35 11.0 58.0 25.0  94.0  not_sel G_42      SC SEMEKI
36 44.0 13.0 43.5 100.5  not_sel G_58 TGx 2000-126GZ
37 12.0 36.0 53.0 101.0  not_sel G_25      S1079/6/7
38 73.0 10.0 24.0 107.0  not_sel G_67   TGx 2002-3FM
39 11.0 76.0 20.5 107.5  not_sel G_46      SC SIGNAL
40 68.0 23.0 18.0 109.0  not_sel G_10           M667
41 55.0  4.5 50.0 109.5  not_sel  G_2           A773
42 49.0 16.0 45.0 110.0  not_sel G_30     S1187/5/25
43 77.0 13.0 21.0 111.0  not_sel G_75   TGx 2014-5GM
44 15.0 53.0 44.0 112.0  not_sel G_92  TGx 2053-15FZ
45 54.0  5.0 54.0 113.0  not_sel G_17           N390
46 10.0 76.0 29.5 115.5  not_sel G_43    SC SENTINEL
47 81.0  5.5 29.0 115.5  not_sel  G_5      CLARK-63K
48 31.0 25.0 60.0 116.0  not_sel G_89  TGx 2047-08FZ
49 33.5 22.0 63.0 118.5  not_sel  G_6           K872
50 65.0 15.0 40.0 120.0  not_sel G_88  TGx 2045-02FZ
51  8.0 76.0 40.0 124.0  not_sel G_34    S1239/6/135
52 30.5 72.0 22.0 124.5  not_sel G_70  TGx 2014-21FM
53 35.0 76.0 16.0 127.0  not_sel G_63   TGx 2001-3FM
54 51.0 76.0  0.5 127.5  not_sel G_27     S1146/5/25
55 47.0 15.5 66.0 128.5  not_sel G_94  TGx 2076-15FZ
56 45.0 60.0 24.0 129.0  not_sel G_35    S1240/6/288
57 50.0 76.0  3.0 129.0  not_sel G_51    SC1146/5/25
58 20.0 76.0 34.0 130.0  not_sel G_26      S1140/5/4
59 59.0 22.5 52.0 133.5  not_sel G_61  TGx 2001-11DM
60 42.0 38.0 57.0 137.0  not_sel G_91  TGx 2052-21FZ
61 39.0 38.0 64.0 141.0  not_sel G_41        SC SAGA
62 86.0 16.0 41.0 143.0  not_sel G_19           O253
63 31.0 40.0 76.0 147.0  not_sel G_84  TGx 2033-85GZ
64 80.0 27.0 42.0 149.0  not_sel G_97  TGx 2090-14FZ
65 32.0 27.0 90.0 149.0  not_sel G_98       TIKOLORE
66 63.0 23.0 65.0 151.0  not_sel G_72  TGx 2014-43FM
67 38.5 21.0 93.0 152.5  not_sel G_65  TGx 2002-35FM
68 33.0 59.0 62.0 154.0  not_sel G_81  TGx 2033-36GZ
69 56.0 64.0 35.0 155.0  not_sel G_85  TGx 2033-91GZ
70 12.5 76.0 67.0 155.5  not_sel G_73  TGx 2014-49FZ
71 58.0 64.0 39.5 161.5  not_sel G_82  TGx 2033-53GZ
72 60.0 64.0 41.0 165.0  not_sel G_90  TGx 2050-01FZ
73 35.5 72.0 58.0 165.5  not_sel G_48      SC SQUIRE
74 40.5 33.0 93.0 166.5  not_sel G_57   TGx 1991-22F
75 43.0 69.0 56.0 168.0  not_sel G_87  TGx 2033-95GZ
76 26.0 55.0 88.0 169.0  not_sel G_76   TGx 2020-1GZ
77 53.0 28.5 89.0 170.5  not_sel G_80  TGx 2033-25GZ
78 42.0 64.0 68.0 174.0  not_sel G_12       Makwacha
79 34.5 62.0 84.0 180.5  not_sel G_95   TGx 2089-3FZ
80 90.0 76.0 15.5 181.5  not_sel G_24   Panorama 358
81 37.5 70.0 75.0 182.5  not_sel G_18         NASOKO
82 84.0 38.0 61.0 183.0  not_sel G_22  Panorama 29 I
83 86.0 63.0 35.5 184.5  not_sel G_71  TGx 2014-33FM
84 86.0 25.5 73.0 184.5  not_sel G_83  TGx 2033-76GZ
85 70.0 38.0 77.0 185.0  not_sel G_78  TGx 2031-03FZ
86 79.0 18.5 90.0 187.5  not_sel G_56   TGx 1987-62F
87 74.0 70.0 45.0 189.0  not_sel G_96   TGx 2089-8FZ
88 81.0 76.0 36.0 193.0  not_sel G_66   TGx 2002-3DM
89 90.0 22.0 81.0 193.0  not_sel  G_7         Kaleya
90 72.0 36.0 86.0 194.0  not_sel G_86  TGx 2033-92GZ
91 45.0 76.0 74.0 195.0  not_sel G_23     Panorama 3
92 90.0 38.0 69.0 197.0  not_sel G_59  TGx 2000-26FZ
93 45.0 76.0 78.0 199.0  not_sel G_37           S882
94 38.0 76.0 85.0 199.0  not_sel G_79 TGx 2033-103GZ
95 45.0 64.0 93.0 202.0  not_sel G_15       MRI DINA
96 90.0 76.0 46.5 212.5  not_sel G_69  TGx 2014-16FM
97 45.0 76.0 93.0 214.0  not_sel G_62  TGx 2001-24FM

Results

Highlighting the ranking of probability of superior performance per trait of the selected families.

Figure 1: Ranking of probability of superior performance per trait

Results

Figure 2: Selected families based on BPSI rank

Title?

  • Selection of superior soybean genotypes across locations and years in Zimbabwe according to multitrait ideotype
  • Multitrait selection of soybean varieties using Bayesian probabilistic selection index
  • josetchagas@usp.br
  • Obrigado!

Referências

Chagas, José Tiago Barroso, Kaio Olimpio das Graças Dias, Vinicius Quintão Carneiro, Lawrência Maria Conceição De Oliveira, Núbia Xavier Nunes, José Domingos Pereira Júnior, Pedro Crescêncio Souza Carneiro, and José Eustáquio de Souza Carneiro. 2025. “Bayesian Probabilistic Selection Index in the Selection of Common Bean Families.” Crop Science 65 (May): e70072. https://doi.org/10.1002/CSC2.70072.
Chaves, Saulo F. S., Matheus D. Krause, Luiz A. S. Dias, Antonio A. F. Garcia, and Kaio O. G. Dias. 2024. “ProbBreed: A Novel Tool for Calculating the Risk of Cultivar Recommendation in Multienvironment Trials.” G3 Genes|Genomes|Genetics 14 (March). https://doi.org/10.1093/G3JOURNAL/JKAE013.
Dias, Kaio O. G., Jhonathan P. R. dos Santos, Matheus D. Krause, Hans Peter Piepho, Lauro J. M. Guimarães, Maria M. Pastina, and Antonio A. F. Garcia. 2022. “Leveraging Probability Concepts for Cultivar Recommendation in Multi-Environment Trials.” Theoretical and Applied Genetics 135 (April): 1385–99. https://doi.org/10.1007/S00122-022-04041-Y/FIGURES/4.